### Abstract

Original language | English |
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Title of host publication | Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids |

Publisher | Springer Verlag |

Number of pages | 1 |

ISBN (Electronic) | 978-3-319-02417-2 |

ISBN (Print) | 978-3-319-02416-5 |

DOIs | |

Publication status | Published - 2014 |

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### Cite this

*Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids*Springer Verlag. https://doi.org/10.1007/978-3-319-02417-2_3

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*Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids.*Springer Verlag. https://doi.org/10.1007/978-3-319-02417-2_3

**Epilogue : SpringerBriefs in Applied Sciences and Technology.** / Siginer, D.A.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Epilogue

T2 - SpringerBriefs in Applied Sciences and Technology

AU - Siginer, D.A.

N1 - Export Date: 20 June 2018

PY - 2014

Y1 - 2014

N2 - A unified field theory for viscoelastic, in particular, nonlinear viscoelastic fluids along the lines of the Navier–Stokes equations for Newtonian fluids is still lacking. Several constitutive structures popularly used are subject to Hadamard and dissipative instabilities as a result of the omission of some fundamental continuum mechanics principles in their derivation as well as thermodynamic principles. Naturally, they have a bearing on the ability of the constitutive formulations in predicting flows in general geometries and for high We. A number of constitutive equations that may be stable in the Hadamard and dissipative sense and are compliant with the principles of thermodynamics predict zero second normal stress differences and thereby cannot be used in describing the transversal field in flows in tubes of arbitrary cross-section.

AB - A unified field theory for viscoelastic, in particular, nonlinear viscoelastic fluids along the lines of the Navier–Stokes equations for Newtonian fluids is still lacking. Several constitutive structures popularly used are subject to Hadamard and dissipative instabilities as a result of the omission of some fundamental continuum mechanics principles in their derivation as well as thermodynamic principles. Naturally, they have a bearing on the ability of the constitutive formulations in predicting flows in general geometries and for high We. A number of constitutive equations that may be stable in the Hadamard and dissipative sense and are compliant with the principles of thermodynamics predict zero second normal stress differences and thereby cannot be used in describing the transversal field in flows in tubes of arbitrary cross-section.

U2 - 10.1007/978-3-319-02417-2_3

DO - 10.1007/978-3-319-02417-2_3

M3 - Chapter

SN - 978-3-319-02416-5

BT - Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids

PB - Springer Verlag

ER -